Is there a starting relay on a 1988 Pontiac Firebird and if so where is it located?

Does it have a coded key? If so, the resistor wires may be broken inside column. To bypass, you can take your key to a stereo shop and have the resistance in the key measured and purchase a resistor. Very cheap. Place the resistor in between the two wires in the orange wrapping coming out of the steering column. If this doesn't fix the problem, look into the neutral safety switch.